.-----. ___________ <-.
v .~`¯`¬. .~'¯¯ ¯¯`-. .~'¯`¬. |
a | A B | b
| '-._.~' `-.__ __.~' `-._.~' ^
`-> ¯¯¯¯¯¯¯¯¯¯¯ `------'
used to analyze the flow of goods and services among sectors in an economy. Developed by professor Wassily Leontief
Shown above in its most simple state, we'll say entity A makes 100 katydidics. entity A, while creating these katydidics, uses an average of 2 katydidics in repairing damaged manufacturing equipment. a = 0.02.
Entity B creates univators. Entity B uses up 4% of its univators in paying off loan sharks
, and raising worker moral. b = 0.04.
A and B are in cahoots, where A gives B all the katydidics they need (c), and B gives A all the univators they can use (d). Creating katydidics is an exhausting process, so A has a high assembly worker turnover rate
. They need approximatly 7 univators for every 100 katydidics that come out the end of the line. d = 0.07.
Creating univators on the other hand is fairly simple, but the katydidics are essential to the process. B only needs 1 katydidic for every 100 univators created. c = 0.01.
Using these values, we can express this system in the weighted digraph
at the top, or we can use a technology matrix
A |.02 .07|
From | |
B |.01 .04|
Now, lets suppose an order is put out, or demand is needed for production of 600 univators
, and 200 katydidics
. We need to know the number of univators and katydidics that must be manufactured.
= 200a + 600c + 200
= 600b + 200d + 600
However, once again, this can grow in complexity exponentially, when new entities are introduced. Assuming we have our technology matrix, T, we can express our order, or demand matrix
| 200 |
D = | |
| 600 |
and our production matrix
| b |
P = | |
| a |
we can find the number of katydidics and univators that need to be produced.
P = TP+D
total production = internal consumption + external demand